Abstract
We consider the problem of learning an acyclic discrete circuit with n wires, fan-in bounded by k and alphabet size s using value injection queries. For the class of transitively reduced circuits, we develop the Distinguishing Paths Algorithm, that learns such a circuit using (ns)O(k) value injection queries and time polynomial in the number of queries. We describe a generalization of the algorithm to the class of circuits with shortcut width bounded by b that uses (ns)O(k + b) value injection queries. Both algorithms use value injection queries that fix only O(kd) wires, where d is the depth of the target circuit. We give a reduction showing that without such restrictions on the topology of the circuit, the learning problem may be computationally intractable when s = n Θ(1), even for circuits of depth O(logn). We then apply our large-alphabet learning algorithms to the problem of approximate learning of analog circuits whose gate functions satisfy a Lipschitz condition. Finally, we consider models in which behavioral equivalence queries are also available, and extend and improve the learning algorithms of [5] to handle general classes of gates functions that are polynomial time learnable from counterexamples.
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Angluin, D., Aspnes, J., Chen, J., Reyzin, L. (2007). Learning Large-Alphabet and Analog Circuits with Value Injection Queries. In: Bshouty, N.H., Gentile, C. (eds) Learning Theory. COLT 2007. Lecture Notes in Computer Science(), vol 4539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72927-3_6
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DOI: https://doi.org/10.1007/978-3-540-72927-3_6
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